Similar Figures and Their AreasName:____________________

Date:__________Warm Up:

1. For the circles below:

A. Find the lengths of their radii

B. Find their circumferences.

C. Find the ratio of their circumferences.

D. Find their areas.

E. Find the ratio of their areas.

2. The floor areas of two similar gymnasiums are rectangles of 14,400 square feet and 6400 square feet.

A. If the length of the floor in the smaller gymnasium is 128 feet, what is the width of the smaller gymnasium?

B. If the width of the larger gymnasium is 75 feet, what is the length of the floor in the larger gymnasium?

C. Draw and completely label a sketch of each gym.

C. What is the ratio of their areas?

D. What is the ration of their perimeter?

6 in

10 in

•O

•P

Notes:

1. What is the relationship between the corresponding angles in similar figures ?

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4.

d. If the mW = 116, ________________ find another angle measure.

e. If XW = 115 cm, _________________ find the length of another segment.

f. If the area of _________________ ABCD = 27 units2, find the area of UVWX.

2. What is the relationship between the corresponding perimeters in similar figures?

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3. What is the relationship between the corresponding areas in similar figures?

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5. EFGHIJ ONMLKJ with NO=3 units and EF = 5 units. The area of EFGHIJ is 32 square units and the perimeter of OMNLKJ is 15 units.

a. What is the area of OMNLKJ? b. What is the perimeter of EFGHIJ?

8. Two quadrilaterals are similar and have perimeters of 33 cm and 22 cm. If the area of the larger quadrilateral is 96 cm2, find the area of the smaller.

6. Stop signs are shaped like regular octagons. A regulation stop sign has sides 32 cm long, while the stop sign for a snowmobile trail has sides 8 cm long. What is the ratio of the areas of the two stop signs?

7. Two right triangles are similar and have areas of 36 m2 and 144 m2. If the hypotenuse of the larger triangle is 30 m long, what is the length of the hypotenuse of the smaller triangle?

9. Two similar ancient Egyptian vases are 1 ft and 2 ft tall. If it takes 1 pint of paint to restore the larger vase, how much paint would the smaller vase require?

10. At the right, ABCD UVWX.

a. What is the ratio of their perimeters? b. What is the ratio of their areas?

11. Two similar rectangles have perimeters of 75 ft and 150 ft, respectively. What is the ratio of their areas?

12. Two similar isosceles trapezoids have areas of 40 and 160 square units. If the longer base of the larger trapezoid has a measure of 14 units, what is the measure of the corresponding base of the smaller trapezoid?

13. Two similar American flags are 2 ft long and 6 ft long. If the area of the red fabric on the smaller flag is 124 In2, what is the area of the red fabric

on the larger one?